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The occupied and unoccupied electronic structures of three high spin TM(acac) 3 (TM = Cr, Mn, and Fe) complexes (I, II, and III, respectively) were studied by revisiting their literature vapour- phase He(I) and, when available, He(II) photoemission (PE) spectra and by means of original near- edge X- ray absorption fine structure (NEXAFS) spectroscopic data recorded at the OK-edge (OK-edge) and TM (L2,3)- edges (TML2,3- edges). The assignments of the vapour-phase He(I)/He(II) PE spectra were guided by the results of spin- unrestricted non- relativistic Slater transition state calculations, while the OK- edge and TM(L2,3)edge spectroscopic pieces of evidence were analysed by exploiting the results of spin-unrestricted scalar-relativistic time-dependent density functional theory (DFT) and DFT/ROCIS calculations, respectively. Although the actual symmetry (D-3, in the absence of any Jahn-Teller distortion) of the title molecules allowed an extensive mixing between TM t(2g)- like and eg- like atomic orbitals, the use of the Nalewajski- Mrozek TM-O bond multiplicity index combined with a thorough analysis of the ground state (GS) outcomes allowed the assessment of the TM-O bond weakening associated with the progressive TM 3d- based e(g)- like orbital filling. The experimental information provided by K-O- edge spectra was rather poor; nevertheless, the combined use of symmetry, orbitals and spectra allowed us (i) to rationalise minor differences characterizing spectral features along the series, (ii) to quantify the contribution provided by the ligand-to-metal-charge-transfer (LMCT) excitations to the different spectral features, and (iii) to recognize the t2g-/eg- like nature of the TM 3d- based orbitals involved in LMCT transitions. As far as the TML2,3- edge spectra and the DFT/ROCIS results were concerned, the lowest lying L-I, II(3) spectral features included states having either the GS spin multiplicity (S(I) = 3/2, S(II) = 2) or, at higher excitation energies (EEs), states with Delta S = +/- 1. In contrast to that, only states with Delta S = 0, -1 significantly contributed to the IIIL3 spectral pattern. Along the whole series, the L-3 higher EE side was systematically characterized by states involving (TM)2p pi(4) MLCT excitations; as such, coupled- single excitations with DS = 0 were involved in I and II, while single MLCT (TM)2p pi(4) transitions with Delta S = -1 were involved in III.

With the help of a recently suggested computational scheme [J. Chem. Phys. 2007, 127, 084101], Mossbauer isomer shifts are calculated within the context of density functional theory, for a series of iron containing compounds. The influence of the choice of a density functional and of the truncation of a basis set on the results of calculations is analyzed. It has been observed that the hybrid density functionals, especially BH&HLYP, provide better correlation with experimental results than pure density functionals. The analysis of basis set truncation reveals that the addition (or removal) of the tightmost primitive functions to a large uncontracted basis set has only a minor influence on the calculated isomer shift values. It is observed that, with the use of a small contracted basis set, a reasonable accuracy for the calculated isomer shifts can be achieved.

This research has benefited from the support of the TMO Cancer Avesian from the Cancer Plan 2009/2013, Action 3.3. H.C gratefully acknowledges the 'Grand Equipement National de Calcul Intensif./Centre Informatique National de l'Enseignement Superieur' (GENCI/CINES) for HPC resources/computer time 507 (Project cpt2130).; International audience; The different fragmentation channels of cytosine, adenine and guanine have been studied through DFT calculations. The electronic structure of bases, their cations, and the fragments obtained by breaking bonds provides a good understanding of the fragmentation process that can complete the experimental approach. The calculations allow assigning various fragments to the given peaks. The comparison between the energy required for the formation of fragments and the peak intensity in the mass spectrum is used. For cytosine and guanine the elimination of the HNCO molecule is a major route of dissociation, while for adenine multiple loss of HCN or HNC can be followed up to small fragments. For cytosine, this corresponds to the initial bond cleavage of N3-C4/N1-C2, which represents the main dissociation route. For guanine the release of HNCO is obtained through the N1-C2/C5-C6 bond cleavage ( reverse order also possible) leading to the largest peak of the spectrum. The corresponding energies of 3.5 and 3.9 eV are typically in the range available in the experiments. The loss of NH3 or HCN is also possible but requires more energy. For adenine, fragmentation consists of multiple loss of the HCN molecule and the main route corresponding to HC8N9 loss is followed by the release of HC2N1.

In this article we explain how the existing linear response theory of time-dependent density-functional theory can be extended to obtain excitation energies in the framework of time-dependent current-density-functional theory. We use the Vignale-Kohn current-functional [G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996)] which has proven to be successful for describing ultranonlocal exchange-correlation effects in the case of the axial polarizability of molecular chains [M. van Faassen, P. L. de Boeij, R. van Leeuwen, J. A. Berger, and J. G. Snijders, Phys. Rev. Lett. 88, 186401 (2002); J. Chem. Phys. 118, 1044 (2003)]. We study a variety of singlet excitations for a benchmark set of molecules. The pi(*)

We present a discrete solvent reaction field (DRF) model for the calculation of frequency-dependent hyperpolarizabilities of molecules in solution. In this model the solute is described using density functional theory (DFT) and the discrete solvent molecules are described with a classical polarizable model. The first hyperpolarizability is obtained in an efficient way using time-dependent DFT and the (2n+1) rule. The method was tested for liquid water using a model in which a water molecule is embedded in a cluster of 127 classical water molecules. The frequency-dependent first and second hyperpolarizabilities related to the electric field induced second harmonic generation (EFISH) experiment, were calculated both in the gas phase and in the liquid phase. For water in the gas phase, results are obtained in good agreement with correlated wave function methods and experiments by using the so-called shape-corrected exchange correlation (xc)-potentials. In the liquid phase the effect of using asymptotically correct functionals is discussed. The model reproduced the experimentally observed sign change in the first hyperpolarizaibility when going from the gas phase to the liquid phase. Furthermore, it is shown that the first hyperpolarizability is more sensitive to damping of the solvent-solute interactions at short range than the second hyperpolarizability. (C) 2003 American Institute of Physics.

In this work we present theory and implementation for a discrete reaction field model within Density Functional Theory (DFT) for studying solvent effects on molecules. The model combines a quantum mechanical (QM) description of the solute and a classical description of the solvent molecules (MM). The solvent molecules are modeled by point charges representing the permanent electronic charge distribution, and distributed polarizabilities for describing the solvent polarization arising from many-body interactions. The QM/MM interactions are introduced into the Kohn-Sham equations, thereby allowing for the solute to be polarized by the solvent and vice versa. Here we present some initial results for water in aqueous solution. It is found that the inclusion of solvent polarization is essential for an accurate description of dipole and quadrupole moments in the liquid phase. We find a very good agreement between the liquid phase dipole and quadrupole moments obtained using the Local Density Approximation and results obtained with a similar model at the Coupled Cluster Singles and Doubles level of theory using the same water cluster structure. The influence of basis set and exchange correlation functional on the liquid phase properties was investigated and indicates that for an accurate description of the liquid phase properties using DFT a good description of the gas phase dipole moment and molecular polarizability are also needed. (C) 2003 American Institute of Physics.

In this work we have investigated the effects of substituting carbon atoms with B and N on the second hyperpolarizability of C60 using time-dependent density functional theory. We have calculated the second hyperpolarizability of the double substitute-doped fullerenes C58NN, C58BB and C58BN. For C60 only small changes in the second hyperpolarizability were found when doping with either 2B or 2N. However, by doping C60 with both B and N, creating an donor-acceptor system, an increase in the second hyperpolarizability with about 50% was found.

Time-dependent density functional theory has been used to calculate the static and frequency-dependent dielectric function e(ω) of nonmetallic crystals. We show that a real-space description becomes feasible for crystals by using a combination of a lattice-periodic (microscopic) scalar potential with a uniform (macroscopic) electric field as perturbation in a periodic structure calculation. The induced density and microscopic potential can be obtained self-consistently for fixed macroscopic field by using linear response theory in which Coulomb interactions and exchange-correlation effects are included. We use an iterative scheme, in which density and potential are updated in every cycle. The explicit evaluation of Kohn–Sham response kernels is avoided and their singular behavior as function of the frequency is treated analytically. Coulomb integrals are evaluated efficiently using auxiliary fitfunctions and we apply a screening technique for the lattice sums. The dielectric function can then be obtained from the induced current. We obtained e(ω) for C, Si, and GaAs within the adiabatic local density approximation in good agreement with experiment. In particular in the low-frequency range no adjustment of the local density approximation (LDA) band gap seems to be necessary.

Density functional calculations on the (non)linear optical properties of conjugated molecular chains using currently popular exchange-correlation (xc) potentials give overestimations of several orders of magnitude. By analyzing ``exact'' and Krieger-Li-Iafrate xc potentials, the error is traced back to an incorrect electric field dependence of the ``response part'' of the xc potential in local and gradient-corrected density approximations, which lack a linear term counteracting the applied electric field.

An accurate determination of frequency-dependent molecular hyperpolarizabilities is at the same time of possible technological importance and theoretically challenging. For large molecules, Hartree-Fock theory was until recently the only available ab initio approach. However, correlation effects are usually very important for this property, which makes it desirable to have a computationally efficient approach in which those effects are (approximately) taken into account. We have recently shown that frequency-dependent hyperpolarizabilities can be efficiently obtained using time-dependent density functional theory. Here, we shall present the necessary theoretical framework and the details of our implementation in the Amsterdam Density Functional program. Special attention will be paid to the use of fit functions for the density and to numerical integration, which are typical of density functional codes. Numerical examples for He, CO, and para-nitroaniline are presented, as evidence for the correctness of the equations and the implementation. © 1998 American Institute of Physics.

Response calculations in the framework of time-dependent density-functional theory ~TDDFT! have by now been shown to surpass time-dependent Hartree-Fock ~TDHF! calculations in both accuracy and efficiency. This makes TDDFT an important tool for the calculation of frequency-dependent ~hyper!polarizabilities, excitation energies, and related properties of medium-sized and large molecules. Two separate approximations are made in the linear DFT response calculations. The first approximation concerns the exchange-correlation ~xc! potential, which determines the form of the Kohn-Sham orbitals and their one-electron energies, while the second approximation involves the so-called xc kernel f xc , which determines the xc contribution to the frequencydependent screening. By performing calculations on small systems with accurate xc potentials, constructed from ab initio densities, we can test the relative importance of the two approximations for different properties and systems, thus showing what kind of improvement can be expected from future, more refined, approximations to these xc functionals. We find that in most, but not all, cases, improvements to v xc seem more desirable than improvements to f xc . @S1050-2947~98!10004-5#

In this paper we present time-dependent density functional calculations on frequency-dependent first (β) and second (γ) hyperpolarizabilities for the set of small molecules, N2, CO2, CS2, C2H4, NH3, CO, HF, H2O, and CH4, and compare them to Hartree–Fock and correlated ab initio calculations, as well as to experimental results. Both the static hyperpolarizabilities and the frequency dispersion are studied. Three approximations to the exchange-correlation (xc) potential are used: the widely used Local Density Approximation (LDA), the Becke–Lee–Yang–Parr (BLYP) Generalized Gradient Approximation (GGA), as well as the asymptotically correct Van Leeuwen–Baerends (LB94) potential. For the functional derivatives of the xc potential the Adiabatic Local Density Approximation (ALDA) is used. We have attempted to estimate the intrinsic quality of these methods by using large basis sets, augmented with several diffuse functions, yielding good agreement with recent numerical static LDA results. Contrary to claims which have appeared in the literature on the basis of smaller studies involving basis sets of lesser quality, we find that the static LDA results for β and γ are severely overestimated, and do not improve upon the (underestimated) Hartree–Fock results. No improvement is provided by the BLYP potential which suffers from the same incorrect asymptotic behavior as the LDA potential. The results are however clearly improved upon by the LB94 potential, which leads to underestimated results, slightly improving the Hartree–Fock results. The LDA and BLYP potentials overestimate the frequency dependence as well, which is once again improved by the LB94 potential. Future improvements are expected to come from improved models for asymptotically correct exchange-correlation potentials. Apart from the LB94 potential used in this work, several other asymptotically correct potentials have recently been suggested in the literature and can also be expected to improve considerably upon the relatively poor LDA and GGA results, for both the static properties and their frequency dependence.

DFT schemes based on conventional and less conventional exchange-correlation (XC) functionals have been employed to determine the polarizability and second hyperpolarizability of π-conjugated polyacetylene chains. These functionals fail in one or more of several ways: (i) the correlation correction to α is either much too small or in the wrong direction, leading to an overestimate; (ii) γ is significantly overestimated; (iii) the chain length dependence is excessively large, particularly for γ and for the more alternant system; and (iv) the bond length alternation effects on γ are either underestimated or qualitatively incorrect. The poor results with the asymptotically correct van Leeuwen-Baerends XC potential show that the overestimations are not related to the asymptotic behavior of the potential. These failures are described in terms of the separate effects of the exchange and the correlation parts of the XC functionals. They are related to the short-sightedness of the XC potentials which are relatively insensitive to the polarization charge induced by the external electric field at the chain ends. © 1998 American Institute of Physics.

The valence photoabsorption spectra of the series of the monoanionic closed shell icosahedral clusters MAu12- with M = V, Nb and Ta have been calculated with the time-dependent density functional theory (TDDFT), employing the zero-order regular approximation (ZORA) at both scalar relativistic and spin orbit coupling levels. The calculated photoabsorption spectra show interesting variations according to the nature of the encapsulated metal atom. Spin-orbit coupling plays an important role in these systems. The comparison with the neutral isoelectronic clusters WAu12 and MoAu12 suggests a curious relationship along the diagonal of the periodic table. (C) 2008 Elsevier B.V. All rights reserved.

Time-dependent density functional theory (TDDFT) coupled to the relativistic two-component zeroth-order regular approximation, both available in the last version of the ADF package, have been successfully used to simulate X-ray absorption spectra of TiCl4, Ti(eta(5)-C5H5)Cl-3, and Ti(eta(5)-C5H5)(2)Cl-2 in terms of their oscillator strength distributions. Besides allowing a first principle assignment of Ti 1s, Cl 1s, and Ti 2p (L-2,L-3 edges) core excitation spectra, theoretical outcomes provide a rationale for deviations from the expected L-3/L-2 branching ratio.

The localized Hartree-Fock and the open-shell LHF (OSLHF) approaches are reviewed and rederived under a unique formalism. Three different treatments of the OSLHF correction term are discussed and results for excitation energies are presented for small- and medium-size closed- and open-shell molecules.

The potentiality of the time dependent density functional theory (TDDFT) for the description of core excitation spectra (XAS) in transition metal oxides is analyzed, considering the rutile form of TiO(2) as a test case. Cluster models are adopted to mimic the bulk, embedded within an array of point charges to simulate the Madelung potential. All of the edges, titanium and oxygen K and titanium L edges, are considered, and the TDDFT results are compared with the experimental data in order to assess the performance of the theoretical approach in dealing with this complex class of compounds. Satisfactory results have been obtained for the Ti and O K edges, while in the case of the Ti L edge some discrepancies with the experiment are still present. The configuration mixing explicitly included in the TDDFT model strongly influences the distribution of the 2p metal oscillator strength. The origin of the spectral features is investigated with the help of the partial density of the virtual states (PDOS) calculated for each core hole considered, which can be qualitatively compared with the theoretical spectra calculated in the Kohn-Sham one-electron approach.

The B-spline linear combination of atomic orbitals method has been employed to study the valence and core photoionization dynamics of SF6. The cross section and asymmetry parameter profiles calculated at the time dependent density functional theory level have been found to be in fairly nice agreement with the experimental data, with the quality of the exchange-correlation statistical average of orbital potential results superior to the Van Leeuwen-Baerends 94 (LB94) ones [Phys. Rev. A 49, 2421 (1994)]. The role of response effects has been identified by a comparison of the time dependent density functional theory results with the Kohn-Sham ones interchannel coupling effects and autoionization resonances play an important role at low kinetic energies. Prominent shape resonances features have been analyzed in terms of 'dipole prepared' continuum orbitals and interpreted as due to a large angular momentum centrifugal barrier as well as anisotropic (nonspherical) molecular effective potential. Finally, the method has been proven numerically stable, robust, and efficient, thanks to a noniterative implementation of the time dependent density functional theory equations and suitability of the multicentric B-spline basis set to describe continuum states from outer valence to deep core states. (c) 2006 American Institute of Physics.

We have performed Time Dependent Density Functional Theory (TDDFT) calculations employing a cluster model of the core excitation spectra of vanadium pentoxide, V2O5. The excitation energies and dipole transition moments are determined for all the core edges, vanadium and oxygen K- and vanadium L-edges, treating them at the same level of accuracy. The agreement between the TDDFT theoretical spectra and the experimental data is rather good, particularly at the V and O K-edges. A quantitative reproduction of the fine pre-edge structures appears more difficult for the V L-edge. The comparison between the TDDFT results and the results obtained at the simpler one electron Kohn-Sham (KS) level indicates that the V and O K edges can be correctly described within a single particle approximation (KS), while the strong modi. cation of the V L-edge structures from the KS to the TDDFT description emphasizes the importance of configuration mixing to treat the metal 2p excitations. The origin of the calculated pre-edge features is analyzed in detail with the help of the atom-projected density-of-states of the unoccupied levels. This analysis emphasizes the V 3d dominant character of the final states in the conduction band, probed by the V L-absorption. The strong octahedral distortion of the V2O5 structure allows the mixing of the 3d state with the V 4p components, which are mapped by the oscillator strength in the V K- edge spectrum. The high intensity of the O 1s transitions reflects the presence of a significant O 2p component in the conduction band.

Photoionization cross sections and angular distributions of silicon tetrafluoride have been calculated in the framework of the time-dependent density-functional theory approach. Both valence and inner shell ionizations have been considered in an extended photon energy range. Calculations have been carried out by using two different exchange-correlation (xc) potentials characterized by the correct asymptotic behavior. Theoretical results obtained with both the van Leeuwen--Baerends and statistical average of orbital potentials (SAOP) xc potentials are compared with photoabsorption, photoionization, and electron-scattering experiments as well as with previous theoretical calculations. It is suggested that even if both xc potentials provide a reasonably good description of the photoionization dynamics, correlation effects are phenomenologically better accounted for by the SAOP xc potential. Overall, the good accuracy attained with the linear combination of atomic orbitals-time dependent density-functional theory method in reproducing the experimental findings for ${\mathrm{SiF}}_{4}$ makes it a promising and powerful method for the characterization of the photoionization dynamics from medium and large-size molecules.

The electronic and molecular properties of interstitial O 3 in SiO 2 have been theoretically studied by coupling the molecular cluster model to the density functional theory. We find that, on passing from the free species to the interstitial one, electronic and molecular structures of O 3 are only slightly perturbed. Moreover, in agreement with the experimental assignment of Skuja et al., it is confirmed that the ubiquitous absorption band at 4.8 eV characterizing 7.9 eV photon-irradiated SiO 2 samples includes a contribution due to excitations between O 3 based occupied and unoccupied MOs.

A discrete solvent reaction field model for calculating frequency-dependent molecular linear response properties of molecules in solution is presented. The model combines a time-dependent density functional theory (QM) description of the solute molecule with a classical (MM) description of the discrete solvent molecules. The classical solvent molecules are represented using distributed atomic charges and polarizabilities. All the atomic parameters have been chosen so as to describe molecular gas phase properties of the solvent molecule, i.e., the atomic charges reproduce the molecular dipole moment and the atomic polarizabilities reproduce the molecular polarizability tensor using a modified dipole interaction model. The QM/MM interactions are introduced into the Kohn-Sham equations and all interactions are solved self-consistently, thereby allowing for the solute to be polarized by the solvent. Furthermore, the inclusion of polarizabilities in the MM part allows for the solvent molecules to be polarized by the solute and by interactions with other solvent molecules. Initial applications of the model to calculate the vertical electronic excitation energies and frequency-dependent molecular polarizability of a water molecule in a cluster of 127 classical water molecules are presented. The effect of using different exchange correlation (xc)-potentials is investigated and the results are compared with results from wave function methods combined with a similar solvent model both at the correlated and uncorrelated level of theory. It is shown that accurate results in agreement with correlated wave function results can be obtained using xc-potentials with the correct asymptotic behavior. (C) 2003 American Institute of Physics.

The polarizabilities of 15 organic molecules are calculated using the Restricted Hartree Fock (RHF) method, the Time Dependent Density Functional Theory (TD-DFT) and the Direct Reaction Field (DRF) approach. The RHF method gives rather poor results, while the other two give average deviations comparable to the experimental uncertainty. The DRF approach is very fast (

Time-dependent density functional theory provides a first principles method for the calculation of frequency-dependent polarizabilities, hyperpolarizabilities, excitation energies and many related response properties. In recent years, the molecular results obtained by several groups have shown that this approach is in general more accurate than the time-dependent Hartree-Fock approach, and is often competitive in accuracy with computationally more demanding conventional ab initio approaches. In this paper, our implementation of the relevant equations in the Amsterdam Density Functional program is described. We will focus on certain aspects of the implementation which are necessary for an efficient evaluation of the desired properties, enabling the treatment of large molecules. Such an efficient implementation is obtained by: using the full symmetry of the molecule, using a set of auxiliary functions for fitting the (zeroth- and first-order) electron density, using a highly vectorized and parallelized code, using linear scaling techniques, and, most importantly, by solving the response equations iteratively.

The electronic structure of both WAu12 and MoAu12 has been calculated at the density functional theory (DFT) level, employing the zero order regular approximation at the scalar relativistic level and including a spin-orbit coupling. The effect of the inclusion of the spin-orbit coupling is discussed, and the differences assigned to the nature of the encaged atom (W or Mo) are identified. Then, the excitation spectra of both clusters are calculated at the time-dependent DFT level, also in this case at both scalar relativistic and spin-orbit levels. The inclusion of spin-orbit coupling is mandatory for an accurate description in the low energy region. At higher energy, where the density of states is higher, the convoluted intensity can be properly described already at the scalar relativistic level. The consequences of the spin-orbit coupling on the excitation spectrum of the clusters indicate that while in WAu12 the lowest excitations are essentially shifted in energy with respect to the scalar relativistic results, in MoAu12, a dramatic splitting in many lines is actually predicted, revealing a quite different behavior of the two clusters.

Valence band and C 1s core-level photoelectron spectra of S-(+)-2-amino-1-propanol (alaninol) and S-(+)-1-amino-2-propanol (isopropanolamine) have been studied by means of synchrotron radiation photoelectron spectroscopy in gas phase. The alaninol, the reduced derivative of the alanine, is a good test system of amino acid-like structures. The isopropanolamine, presenting the inversion of the two functional groups of the alaninol at the chiral carbon, offers the opportunity to study the effect of -OH and -NH(2) structural position on the photoelectron spectra. The influence of the conformational contribution on the electronic structure and the photoelectron spectra has been interpreted using density functional and ab initio theoretical calculations. Agreement has been achieved by taking into account the presence, in gas phase, of two conformers with different population ratios in both chiral systems. The C 1s core-level spectra of alaninol and isopropanolamine are reported and the peak positions of the three carbon atoms of the molecules are assigned.

Correlation in the photoionization dynamics of carbon tetrafluoride is studied in the framework of the time-dependent density-functional. theory (TDDFT) approach by employing a multicentric basis set expansion of the scattering wave function linear combination of atomic orbitals (LCAO) TDDFT. Results obtained with the statistical average of orbital potentials and LB94 exchange-correlation (xc) potentials are compared with photoabsorption, photoionization, and electron-scattering experiments as Well as with past theoretical calculations. Inadequacies in both the V-xc parametrizations employed have been suggested from the analysis of the intensity plots for the (D) over tilde (2)A(1) ionization. The formation of resonant scattering states in selected continuum channels has been studied through the analysis of the dipole-prepared scattering wave function; our findings are then compared with results of electron-scattering calculations. Overall, the LCAO-TDDFT results highlight the effectiveness of the approach for the calculation of the unbound spectrum of fairly large molecules. (c) 2006 American Institute of Physics.

It is demonstrated that the LYP correlation functional is not suited to be used for the calculation of electron spin resonance hyperfine structure (HFS) constants, nuclear magnetic resonance spin-spin coupling constants, magnetic, shieldings and other properties that require a balanced account of opposite- and equal-spin correlation, especially in the core region. In the case of the HFS constants of alkali atoms, LYP exaggerates opposite-spin correlation effects thus invoking too strong in-out correlation effects, an exaggerated spin-polarization pattern in the core shells of the atoms, and, consequently, too large HFS constants. Any correlation functional that provides a balanced account of opposite- and equal-spin correlation leads to improved HFS constants, which is proven by comparing results obtained with the LYP and the PW91 correlation functional. It is suggested that specific response properties are calculated with the PW91 rather than the LYP correlation functional. (c) 2005 American Institute of Physics.